Fractions, Decimals, and PercentsThe BMX rider in the picture is one quarter of the way through a race course.Her time at this point is 4 min, 52.9 s.When training in hot weather, riders need to make sure they keep up their ﬂuid levels.Losing 4 to 5 percent of body mass through sweat can seriously decrease a rider’sperformance. Further dehydration may cause illness.Fractions, decimals, and percents are used in many sports, as well as in other aspects of dailylife. When you get a test score back, you might change it to a percent so you can compare itto your other test results. You often think of money in both decimals and fractions. Forexample, 1.25 is one whole dollar plus a quarter.In this chapter, you will learn how fractions, decimals, and percents are related and usethem to solve problems.What You Will Learnφto compare and order fractions, decimals,and percentsφto convert among fractions, decimals, andpercentsφto relate fractions to terminating orrepeating decimal numbersφto solve problems involving percentsKey Wordspercentrepeating decimalterminating decimalMATH LINKHow are fractions, decimals, and percentsused in the media? Start collectingnewspaper headlines, articles, andadvertisements that show diﬀerent waysto use fractions, decimals, and percents.122NEL Chapter 4esHeadlin%rops by 1 GST D Young 7 OutDerby Wrticipateents Paf 10 Studoainbow.65 kg Rtches 2inner Cain FundTroutRaising
;DA967A:H /-ÌÕ ÞÊ/ Make the following Foldable to organizewhat you learn in Chapter 4.Step 1 Collect three sheets of paper andplace them 2 cm apart. Keep theedges straight.Step 2 Fold the bottom edge of thepaper. Stop 2 cm from the topedge. This makes all tabs thesame size. Staple together alongthe fold.Step 3 Label the tabs.Chapter 4: Fractions, Decimals, and PercentsKey Words126.96.36.199What I Need to Work OnLiteracyLinkAs you work through Chapter 4, takenotes under the appropriate tab.Include information about the keywords, examples, and key ideas.ChapterChapter 4 NEL123
Connect Fractions, Decimals,and PercentsFocus on After this lesson, youwill be able to φ estimate percentsφφas fractions or asdecimalscompare andorder fractions,decimals, andpercentsestimate andsolve problemsinvolving percentpercent means “out of 100” 30% means 30 out of30 or 0.30.100 or100Kim likes to do research on the Internet before he travels. He has founda video of orcas, or killer whales, migrating off the coast of BritishColumbia. The video is 20 megabytes, and 25% has alreadydownloaded. How many megabytes is that?How can you estimate percents? cardboard or index cardrulerscissors25-cm length of ribbonor paper strip (at least1 cm wide)felt markertape124NEL Chapter 4You can use a visual model like an Internet loading strip to help makereasonable estimates of percent and corresponding number values.1.Cut a piece of index card orcardboard to make a rectangle thatis 5 cm by 12 cm. Cut a slot 1.5 cmin from each end of your cardboard.Make each slot slightly longer thanthe width of the ribbon or paperstrip you will use in step 3.12 cm5 cm
2.Use a ruler to draw a 10-cm line between the slots, justabove the top end of the slots. Label 0% and 100%.3.Draw a line at the 12.5-cm point on your ribbon or paperstrip. Colour exactly one half of the ribbon with a marker,so you have a two-colour ribbon.4.Thread the ribbon or paper strip through the slots. Connectthe ribbon tightly at the back. You have now created a“loading-strip model.” You can pull the coloured part ofyour ribbon loop back and forth to show different percentsof coloured ribbon.Set your loading-strip model to show 50%.b) What fraction of the ribbon shown is coloured?What is this fraction as a decimal number?5. a)6.You can use your loading strip to estimate a percent of anumber, such as 50% of 20.a) Write 0 below the 0% end of your loading strip.b) Write 20 below the 100% end of your loading strip.c) How could you use your answer to 5b) to estimate50% of 20? Mark your estimate below the ribbonon your loading strip.0%100%0%100%0%100%0?20Set your loading-strip model to show 25%.b) What fraction of the ribbon shown is coloured? What isthis fraction as a decimal number?c) How could you use your answer to #7b) to estimate25% of 20?7. a)Reﬂect on Your Findings8.How could you use your loading-strip model to estimate75% of 20?75% is 50% 25%.4.1 Connect Fractions, Decimals, and Percents NEL125
Use your money skills to think about fractions, decimals, and percents. 0.251 of a dollar425% of a dollar 0.10 0.501 of a dollar250% of a dollar1 of a dollar1010% of a dollarExample 1: Find a Percent of a NumberFour brothers bought their mother a birthday present for 84.60.They each paid 25% of the bill. How much was each brother’s share?b) Ten co-workers are buying Ted a going away present and will eachpay 10%. They decide to buy him a backpack for 92.30, includingtax. How much should each pay?a) 84.60 2 42.30Solutiona) Find 50% of 84.60.50% of 84.60 is half of 84.60.Half of 84.60 is 42.30.Now find 25% of 84.60.25% is half of 50%.Half of 42.30 is 21.15. 42.30 2 21.15So, 25% of 84.60 is 21.15.Check: 21.15 4 84.60Each brother’s share is 188.8.131.52% is also4I could havedivided by 4. 84.60 4 21.15b)Find 10% of 92.30.10Recall that 10% 1001 1010% of 92.30 is one tenth of 92.30.One tenth of 92.30 is 9.23.Each co-worker should pay 9.23.a)b)c)126NEL Chapter 4Find 50% of 45.80.Find 25% of 50.00.Find 10% of 72.40.0%50%100%0? 84.600%25%50%100%0? 42.30 84.60 92.30 10 9.23
Example 2: Find the Percent of a Number MentallyWhat is 75% of 80?SolutionMethod 1: Use Percents You Know50% of 80 is half of 80.Half of 80 is 40.25% is half of 50%.Half of 40 is 20.75% is 50% 25%.0%25%50%0204075% 100%?8075% of 80 40 20 60So, 75% of 80 is 60.Method 2: Think of a Model80 is., so divide the blocks into 4 groups.75% is 34Each group has, or 20.StrategiesWhat other methodcould you use?Count the number of blocks in 3 groups.Three groups will have 3 20 or 60.So, 75% of 80 is 60.Use mental math to find each percent.a) 75% of 16b) 60% of 90c) 40% of 804.1 Connect Fractions, Decimals, and Percents NEL127
A iZgVXnExample 3: Compare Fractions, Decimals, and PercentsA c 3, 70%, and 0.72. Write them in ascending order.Compare4Ascending ordermeans from least togreatest.SolutionExpress all three values in decimal form.3is 0.75.470% is 0.700.72 is 0.72Compare 0.75, 0.70, and 0.72.0.70 0.72 0.75Descending ordermeans from greatestto least.So, 70% 0.72 34Compare place values.Look at the hundredths place.70% 0.7203410.5Write each set of numbers in ascending order using the symbol.39 , 0.36a) 56%, 0.48, 1b) 35%,2100 A visual model can help you solve problems involving percents. Every percent has an equivalent decimal and fraction value.50%25%10%25% is 0.25 or 1450% is 0.50 or 12110% is 0.10 or10 You can use place value or a number line to comparefractions, decimals, and percents.11 is between 45% and 0.53.45% 2 0.5321 0.5345% 200.5128NEL Chapter 445% is 0.451 is 0.521
How could you find 60% of 120? Explain using diagrams or aloading-strip model.b) Can you find 60% of 120 in more than one way? Explain.1. a)Your friend missed the lesson on understanding how to find 25% of anumber. Explain at least two ways to visualize or understand 25%.b) Show your friend how to find 12.5% of a number.2. a)3.You know how to mentally find 10% and 25% of a number. Write at leastthree other percent amounts you could find using that knowledge.4.How could you mentally find 1% of a number?For help with #9 to #11, refer to Example 2 onpage 127.For help with #5 to #8, refer to Example 1 onpage 126.5.What is 50% of each quantity?a) 134 marblesb) 46 cookiesc) 74.80d) 65.4 m6.What is 25% of each quantity?a) 68 daffodilsb) 7.2 cmc) 42 mind) 0.567.What is 10% of each quantity?a) 15 minb) 34 cmc) 50 catsd) 89.508.Show how to find each amount.a) 50% of 44b) 25% of 20c) 10% of 12d) 1% of 1509.Show how to find eachamount mentally.a) 60% of 40b) 75% of 44c) 20% of 750d) 35% of 24010.Show how to find eachamount mentally.a) 75% of 60b) 35% of 120 mc) 85% of 280 studentsd) 30% of 45 cm11.Describe how you could find 37.5% of 68using only the ability to divide in half andto perform addition. Show your numbersfor each step.4.1 Connect Fractions, Decimals, and Percents NEL129
For help with #12 to #18, refer to Example 3 onpage 128.12.Change each percent to a decimal number.a) 42%b) 38%c) 15% d) 73%14.Compare the numbers in each set. Writethem in ascending order.1 , 0.1214%,1041 , 40%, 0.39c)100a)b)03 , 0.3532%,10, 45%, 0.54c) 12b)76%, 0.72, 34Use the number line to help answer thequestions below.025%50%75%20.According to an article in the newspaper,35% of Regina residents like winter. If thepopulation of Regina is 178 000, howmany people like winter? Show twodifferent ways to find the answer.21.Your bill at a restaurant is 28. You wantto leave a 15% tip. How could youcalculate the amount mentally?22.Carey found that35% of the studentsin her school readfantasy books. Ifthere are 840students in theschool, how manystudents readfantasy books?23.John’s mass was 62 kg last year. If hismass increased by 10% this year, whatis his current mass?24.Three years ago,Sam’s height was108 cm. Since thattime he has grown25% in height.a) How much hashe grown?b) How tall is henow?a)17.On each number line, which number iscorrectly placed? How do you know?a)27.3 28.5 3126b)3015780130NEL Chapter 4340.18122In Australia, the GST is 10%. How wouldyou estimate the GST on items you mightbuy on holiday in Australia?100%What is a fraction between 25% and50%? How do you know?b) What is a decimal number between 0%and 25%?c) What is a decimal number between 75%and 100% that is closer to 75%?119.Compare the numbers in each set. Writethem in descending order.a)16.1, 0.2427%,4What decimal number could be placed atA on the number line? Justify your answer.AChange each percent to a decimal number.a) 57%b) 30%c) 5%d) 88%13.15.18.
25.Clare saved 25% more than Rita. Howmuch did Clare save if Rita saved 288.60?26.Arrange the following numbers indescending order. Show your answerusing both a labelled number line andthe symbol.1, 0.41, and4%,371241027.JuniorSizeJumboSizeKongSize10 20 25 2 4 6 Juice30 50 80 Syrup5 6 8 IngredientTapioca28.At a concert, 60% of the seats wereoccupied. 520 seats were empty. What is thetotal number of seats in the concert hall?29.Figure ABCD is a rectangle with thedimensions shown. What percent of thefigure is shaded? Justify your response.25 mBrannon runs a bubble tea café inWinnipeg. The table shows the cost ofingredients for one drink. The prices are 3.50, 4.50, and 5.50 for each of thethree different sizes.Cost to MakeAt a concert, 75% of the seats were filled.60% of the audience was female. If thereare 3200 seats in the concert hall, howmany in the audience were female? Explain.A30.IceWhat is the cost for making eachsize drink?b) What is the profit for each size ofdrink sold?c) On an average day, Brannon sells80 Junior size, 250 Jumbo size, and120 Kong size drinks. What is theexpected profit for the day?a)Web LinkBubble tea originated in Taiwan in the 1980s andwas ﬁrst sold in Canada in the 1990s. For moreinformation about the history of bubble tea, goto www.mathlinks7.ca and follow the links.B12 mDE 10 m C6gi A c Create a personal logo from two triangles, two rectangles, and two circles.Your logo can resemble a person, animal, or thing. You can cut any of the six shapes, but only into halves or quarters (50% or 25%)of the original shape. You must use all of the triangles, rectangles, and circles or their parts in your logo. Pieces may overlap. Decorate and colour your logo. Label each part shape with its fraction, decimal, or percent equivalent.4.1 Connect Fractions, Decimals, and Percents NEL131
Fractions, Decimals, and PercentsFocus on After this lesson, youwill be able to φ convert amongφφφfractions, decimals,and percentsestimate percentvaluesdistinguishbetweenterminating andrepeating decimalsrelate fractions toterminating andrepeating decimalsIndividual statistics from sporting events are often reported as percentsor decimal numbers. It may be necessary to convert among fractions,decimals, and percents to better understand these statistics.How can you convert among fractions, decimals, andpercents?1.SportsLinkAlthough the statisticis called “savepercentage,” theresult is a decimalnumber.132NEL Chapter 42.Look at the statistics inthe table. Which hockeygoalie do you think ishaving the best season?Why?GoalieShots on GoalSavesA. Auld673606M. Fernandez586545M. Kiprusoff797726D. Hasek709658Goalies can be rated on “save percentage.” This statistic is the ratioof saves to shots on goal.Number of savesSave percentage Shots on goala)Copy the table into your notebook. Extend the table to includetwo more columns.
In the first new column, write the save percentage for eachgoalie as a fraction.c) In the second new column, write the save percentage as adecimal to the nearest thousandth.d) Decide which goalie is having the best season. Explain.b)How does the save percentage help you determine agoalie’s performance?b) Is it better to have a higher or a lower save percentage?Explain why.3. a)4.The ﬁrst Canadianhockey sticks weremodelled on Irishhurley sticks andwere made bythe Mi’kmaq inEastern Canadaover 100 years ago.The save percentage is usually stated as a decimal.a) How are the decimal and fraction forms of the save percentage related?b) Which form is more useful? Why?c) Is either form an actual percent value?Reﬂect on Your Findings5.Summarize methods you can use toa) convert a fraction to a decimalb) convert a decimal to a percentExample 1: Convert From Fractions to Decimals and PercentsThe following data were gathered one season for three National BasketballAssociation (NBA) teams.TeamWinsLossesMiami5923New Jersey4240Los Angeles3448A statistic called “team percentage” is the ratio of team wins to total games.Number of winsTeam percentage Total games playedWhat is the team percentage for each team? Leave your answeras a fraction.b) Change each fraction to a decimal number rounded to the nearestthousandth.c) Use your rounded decimal value to show the approximate percent valuefor each team.a)4.2 Fractions, Decimals, and Percents NEL133
Solutiona) Total games wins lossesMiami:Total games 59 23 82Team percentage 5982New Jersey:Total games 42 40 8242Team percentage 82Los Angeles:Total games 34 48 82Team percentage 3482b) Convert each fraction to a decimal.Miami:59 0.720C 59 82 0.719512191.820.71950.719New Jersey:42 0.512820.720C 42 82 0.512195121.0.51210.512Los Angeles:34 0.415820.513C 34 82 0.414634146.0.41460.414c)0.415NEL Chapter 4The digit to the right ofthe thousandths placeis 1, so round down.The digit to the right ofthe thousandths placeis 6, so round up.To convert to a percent, multiply the decimal by 100.Miami team percentage 0.72 100% 72%New Jersey team percentage 0.512 100% 51.2%Los Angeles team percentage 0.415 100% 41.5%134The digit to the rightof the thousandthsplace is 5, so round up.
Convert each fraction to a decimal number. Round each decimalnumber to the indicated place value. Then, convert to a percent.27 (tenths) b)125 (thousandths) c)1496 (hundredths)a)563962005Example 2: Change Fractions to Repeating DecimalsSome common fractions may change to repeating decimal numbers.These decimal numbers contain one or more digits that repeat overand over without ending.Use a calculator to change each fraction to a repeating decimal.a) 1b) 5c) 5396Solution1 1 3a)3 0.3repeating decimal a decimal number witha digit or group ofdigits that repeatsforever repeating digits areshown with a bar,e.g., 0.777 0.7C 1 3 0.333333333Use a bar over the 3 toshow the repeating part.b) 59 5 9The calculator shows the ﬁnaldigit as 6 because it roundsup. It would show more 5s if ithad a larger display.C 5 9 0.555555556 0.5c)5 5 66C 5 6 0.833333333 0.83Place a bar over only the 3since the 8 does not repeat.Show the following fractions as repeating decimals.2 b) 7a)394.2 Fractions, Decimals, and Percents NEL135
Example 3: Estimate PercentsPaige has answered 94 questions correctly out of 140 questions.Estimate her mark as a percent.SolutionThink: What is 50% of 140?Half of 140 is 70.0%Think: What is 10% of 140?140 10 14StrategiesGuess and CheckRefer to page xvi.60%50% 70%100%70 84 9894140Add 50% and 10% parts together to estimate.50% 10% 60% of 14070 14 84Too low.50% 10% 10% 70% of 14070 14 14 98Too high.The answer is between 60% and 70% but closer to 70%.Estimate each of the following as a percent.a) 23 out of 80b) 421 out of 560Example 4: Change Terminating Decimal Numbers to Fractionsa)b)terminating decimal a decimal number inwhich the digits stop examples include 0.4,0.86, 0.125What fraction of a dollar is 0.75?Change 0.652 to a fraction.Solutiona) The decimal number 0.75 is a terminating decimal . The last digit isin the hundredths place, so the denominator is 100.750.75 0.75 is 75 1003 of a dollar.75 of a dollar orSo, 0.75 is1004b)The 2 is in the thousandths place, so thedenominator is 1000.6520.652 1000Change each terminating decimal number to a fraction.a) 0.48b) 0.078136NEL Chapter 43 quarters
To change a fraction to a decimal number,divide the numerator by the denominator.3 3 88 0.375 Repeating decimal numbers can be writtenusing a bar notation.1 0.333 3 0.3 To express a terminating decimal number as a fraction,use place value to determine the denominator.95914630.9 0.59 1.463 101001000 You can use mental math to estimate percents.Express 0.7 and 0.67 as fractions.b) How are the number of digits after the decimal point for each numberrelated to the number of zeros in the denominator of each fraction?Explain.1. a)2.Vernon was asked to estimate 63 out of 160 as a percent. He said the answerwas between 40% and 50%. Do you agree? Justify your answer.3.Eleven out of 15 calves born on a ranch in one week had white faces. Whatpercent of the calves born that week had white faces? Round your answer tothe nearest tenth of a percent. Show how you got your answer.4.Kanisha said that 0.6555 could be written as 0.65 using bar notation.What mistake has she made? Show how she could write the answer correctly.43c)50For help with #5 to #7, refer to Example 1 onpage 133.5.Use a calculator to change each fraction toa decimal number. Round to the placevalue ths)d) 197289(thousandths)Use a calculator to change each fraction toa decimal number. Round to the placevalue indicated.171 (thousandths)b)(tenths)2528019 (thousandths)43 (hundredths) d)c)6031311a)4.2 Fractions, Decimals, and Percents NEL137
7.A baseball player’s batting average is theratio of number of hits to times at bat. It isusually expressed as a decimal number.of hitsBatting average NumberTimes at batThe following data arefor one baseball season.PlayerTimes at BatHitsA605194B624197What is the batting average for eachplayer? Round each answer to thenearest thousandth.b) Which player had a better battingaverage for the season? Justify yourresponse.a)For help with #12 and #13, refer to Example 3 onpage 136.12.Estimate each of the followingas a percent.a) 36 out of 70b) 125 out of 30013.Estimate each of the followingas a percent.a) 275 out of 500b) 46 out of 90For help with #14 and #15, refer to Example 4 onpage 136.14.Change each decimal number to a fraction.a)15.0.95b)0.3c)0.243d)0.08Change each decimal numbers to a fraction.a) 0.80b) 0.2c) 0.18d) 0.455For help with #8 to #11, refer to Example 2 onpage 135.8.Write each repeating decimal numberusing bar notation.a) 0.5555555 b) 0.090909 c) 0.1877777 d) 2.0151515 9.Write each repeating decimal numberusing bar notation.a) 0.4444444 b) 0.2666666 c) 0.1851851 d) 1.0626262 10.Change each fraction to a repeatingdecimal. Then use bar notation to showthe repeating part.5a)611.345c)997d)11Change each fraction to a repeatingdecimal. Then use bar notation to showthe repeating part.1a)6138b) 2b) 37NEL Chapter 425c)994d)1116.Express the value of each coin as afraction of a dollar. Write the fractionsin ascending order.b) Express the value of each coin as adecimal number. Write the decimalnumbers in ascending order.c) Write a statement using percent thatcompares the three coins.a)17.For each of the following statements,rewrite each percent or decimal as afraction.a) 0.71 of Earth’s surface is coveredwith water or ice.b) Matthew’s batting average is .421.c) Nitrogen makes up approximately78% of the air we breathe.
18.There are 81 girls and 59 boys in RiverCity Day Care.a) Estimate the percent of the children inthe day care that are girls.b) Show how you made your estimate.19.A small town in southern BritishColumbia has a population of 270. Ofthese people, 85 are over the age of 60.a) Estimate the percent of the town’spopulation that is older than 60.b) Show the number of people over 60 asa fraction of the town’s population.Express your fraction as a decimalnumber correct to 3 decimal places.c) What is your decimal value from b)expressed as a percent? How does thisvalue compare with your estimate in a)?20.Rachel and Tim notice a pattern whenchanging ninths into decimal numbers.Here is what they see on their calculator.1 0.1111111193 0.33333333921.Look at each repeating decimal and itsfraction equivalent.4 0.363636. 3699 11654 0.545454. 99 117 0.636363. 6399 11a) What would the fraction equivalentbe for 0.272727 ? 0.909090 ?0.818181 ?b) Write a rule to convert each repeatingdecimal to a fraction. Hint: Write therepeating decimals using bar notation.c) Write four other repeating decimalsthat would follow the same pattern.22. a)2 0.222222229Without dividing, what do you think4 is as a decimal number? Write your9answer using bar notation.b) Predict the decimal equivalent for 8 .9Check your answer using a calculator.a)MATH LINKEach of the headlines shown contains a fraction, a decimal,or a percent.Which headlines would be better written using a diﬀerentrepresentation? Rewrite them with a more appropriaterepresentation. Explain your reasoning.Use a calculator to find repeatingdecimal numbers for3, 45, and6.1,2,,b)7 7 7 7 77Add the numbers in the first half ofeach repeating part to the numbersin the last half. For example,1 0.142857, so add 142 to 857.7c) What pattern did you find?d) What do you think will happen with7 ?4 ? Do you get the same results?13 11HeadlinesSales Up 0.06 Baseball Ticket Profits Fall 31%Role Models22ens See Parents as –––0 of Young Tees410Serious Head InjuriCan Prevent ––5 Bicycle Helmetsby 0.25 Prices IncreaseNewspaperdians Read a Dailyna Almost 0.5 Ca4.2 Fractions, Decimals, and Percents NEL139
Applications of PercentsMike’s mother is taking him with his friends Tran and Gerry to ago-kart track in Saskatoon for his birthday.Focus on After this lesson, youwill be able to.φ estimate answersφto percentcalculationssolve percentproblemsHow can you apply percents to solve problems?1.The sign shows the cost of go-karting.What is the cost per lap if you purchasethe 20-lap package?2.laps for 30.00Tran was not sure if he will like gokarting so he asks for tickets for 5 lapsonly. The other three each choose the 20-lap tickets. Estimate,and then calculate, the total cost of the tickets before tax.3.An adult and three children qualify for the 25% family discount.a) Calculate the amount of the discount.b) What is the total cost of the tickets after the discount?4.GST is added to the cost of go-karting.a) What percent is the GST in Canada?b) Use your knowledge of percent to estimate the amount of GST.c) Use a calculator to find the exact amount of the GST to beadded to the go-karting bill.d) What is the total cost of the tickets, including tax?WelcomeToFuntrack 1.75/lap or 20LiteracyLinkGST means Goodsand Services Tax.PST means ProvincialSales Tax.140NEL Chapter 4
5.Each person is required to wear a helmet. Helmet rental is 5.00plus GST and PST.a) What is the cost to rent four helmets before tax?b) The PST in Saskatchewan is 5%. How much PST and GST ischarged to rent four helmets?c) What is the cost to rent four helmets, including tax?6.What is the total cost for go-karting?Reﬂect on Your Findings7. a)What total amount of tax is charged in your area?Describe how you could estimate the total tax on a purchasein your area. Would your estimate be high or low?c) How could you estimate and calculate a discount?b)Example: Use Percents to Make ComparisonsLauren bought and planted two packages of flowerseeds to use in her science fair project. Package Acontained 44 seeds of which 32 grew into plants.Package B contained 36 seeds of which 27 grewinto plants. Which package of seeds was better?SolutionMethod 1: Estimate the PercentsUse mental math techniques to estimate the percent of growth.Package A:32 out of 44 seeds grew.50% of 44 is half of 44.Half of 44 is 22.25% is half of 50%.Half of 22 is 11.50% 25% 75%A little high.22 11 33Package B:27 out of 36 seeds grew.50% of 36 is half of 36.Half of 36 is 18.25% is half of 50%.Half of 18 is 9.50% 25% 75%18 9 27A little less than 75% of theseeds from Package A grew.Exactly 75% of the seedsfrom Package B grew.0%50%75%100%0182736Package B was better than Package A.4.3 Applications of Percents NEL141
Method 2: Calculate the PercentsPackage A:When you round adecimal value, thenumber becomesapproximate.Package B:C 32 44 0.72727272732 0.7244 0.727 to 3 decimal places0.727 72.7%C 27 36 0.7527 0.75360.75 75%Package A had 72.7% growth.Package B had 75% growth.Since 75% 72.7%, Package B was better than Package A. Decimal numbers and percents are often easier to compare thanfractions. When you round a decimal value, the number becomes approximate.Fractions are exact numbers.Measure the heights of yourself, a friend, and the classroom door.b) Explain how to estimate your height as a percent and as afraction of the door height.c) How can you calculate your height as a percent and as a fractionof the door height?d) Check your suggestions for b) and c) with the height of yourfriend. Do they work?1. a)1422.Bruce is practising throwing darts. He hits the bulls-eye 26 timesout of 40 shots.a) Show this result as a fraction, a decimal number, and a percent.b) Which type of number do you think is best to explain his results?Justify your response.3.Carly and Shannon are practising their free-throw shots. Carlymakes 23 out of 25 shots. Shannon makes 18 out of 20 shots.a) Show each girl’s result using a fraction, a decimal number, anda percent.b) Which type of number is best to compare their results? Explainwhy.NEL Chapter 4
4.Estimate which percent is larger.Then calculate each percent.a) 50% of 184 or 25% of 208b) 10% of 640 or 1% of 325c) 35% of 140 or 70% of 605.1% of a number is 5.40.a) What is 10% of the number?b) What is 25% of the number?c) What is 100% of the number?d) How is the answer in c) related to theanswer in b)?8.Natalie volunteers in the communitylibrary. On Tuesday, 378 people visited thelibrary, and 342 people signed out books.On Thursday, 480 people visited thelibrary, and 420 people signed out books.On what day did a greater percent ofpeople sign out books?9.Desmond wants to list the foods shown indescending order according to the percentof protein content.FoodFor help with #6 and #7, refer to the Example onpages 141–142.Melissa’s father bought two groups ofchicken eggs to hatch for his kindergartenclass. First he bought 28 eggs of which 14hatched. Then he bought 36 eggs of which20 hatched. Which group of eggs was better?Roast turkey1884Ground beef30142Almonds1045Tuna32150What is the percent of protein foreach food? Give your answers to thenearest tenth of a percent.b) Arrange the foods in descending orderof their percent of protein content.a)10.A vacation package at a travel agencycosts 1240. The package is advertisedat 20% off. What is the new price of thepackage? Show your reasoning.11.A snowboard shop is clearing last year’sstock at 35% off.SALEFF!35% O 199.996.Protein (g) Mass of Food (g)7.A school librarian placed two orders fornew books. There were 68 books in thefirst order of which 24 were adventurenovels. There were 82 books in the secondorder of which 35 were adventure novels.Which order of books had the greaterpercent of adventure novels?Estimate the amount of discount forboots that were regularly priced at 199.99.b) Calculate the amount of discount.c) What is the final sale price before tax?a)4.3 Applications of Percents NEL143
12.13.14.A transit company wants to raise its faresby 15% beginning April 1st. Currentticket prices are 1.90 for adults and 1.40 for students.a) What is the exact value of eachincreased ticket price?b) Transit officials want to have ticketprices ending in 0 or 5. Do you thinkthis is a good idea? Explain.c) What are the increased ticket pricesrounded to the nearest multiple of 5?Naomi is the manager of a restaurantin Yellowknife. Her annual salaryis 40 691.00. After a performance review,her boss awards her a pay raise of 8.5%.a) What is the amount of her salary increase?b) What is her new annual salary?The chart shows the weekly pay fora number of part-time workers. Eachworker gets a pay raise as shown.WorkerWeekly PayWeekly Pay RaiseMeagan 210.00 30.00Carl 378.95 45.50Billi 410.50 41.55Which worker received the largestdollar increase?b) What is the percent increase for eachworker? Give each answer to thenearest tenth of a percent.c) Which worker received the largestpercent increase?a)144NEL Chapter 415.The chart gives the lengths of someWestern Canadian rivers.RiverLength (km)Churchill1608Fraser1368MacKenzie1800North Saskatchewan1392Thelon904What is the length of the Fraser Riveras a percent of the l
to use fractions, decimals, and percents. What You Will Learn Æ to compare and order fractions, decimals, and percents Æ to convert among fractions, decimals, and percents Æ to relate fractions to terminating or repeating decimal numbers Æ to solve problems involving percents Key Words pe